Assume the speed of vehicles along a stretch of I-10 has an approximately

normal distribution with a mean of 71 and a standard deviation of 8mph.

a.Ã‚Â Ã‚Â Ã‚Â The current speed limit is 65 mph. What is the proportion of

vehicles less than or equal to the speed limit?

b.Ã‚Â Ã‚Â Ã‚Â What proportion of the vehicles would be going less than 50 mph?

c.Ã‚Â Ã‚Â Ã‚Â A new speed limit will be initiated such that approximately 10% of

vehicles will be over the speed limit. What is the new speed limit based on

this criterion?

d.Ã‚Â Ã‚Â Ã‚Â In what way do you think the actual distribution of speeds differs

from a normal distribution?

#2

A group of students at a school takes a history test. The distribution is

normal with a mean of 25, and a standard deviation of 4.

a.Ã‚Â Ã‚Â Ã‚Â Everyone who scores in the top 30% of the distribution gets a

certificate. What is the lowest score someone can get and still earn a

certificate?

b.Ã‚Â Ã‚Â Ã‚Â The top 5% of the scores get to compete in a statewide history

contest. What is the lowest score someone can get and still go onto compete

with the rest of the state?

#3

Use the normal distribution to approximate the binomial distribution and

find the probability of getting 15 to 18 heads out of 25 flips. Compare this

to what you get when you calculate the probability using the binomial

distribution. Write your answers out to four decimal places.

#4

The patient recovery time from a particular surgical procedure is normally

distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

What is the median recovery time?

a.Ã‚Â Ã‚Â Ã‚Â 2.7

b.Ã‚Â Ã‚Â Ã‚Â 5.3

c.Ã‚Â Ã‚Â Ã‚Â 7.4

d.Ã‚Â Ã‚Â Ã‚Â 2.1

#5

Height and weight are two measurements used to track a child's development.

The World Health Org measures child development by comparing the weights of

children who the same height and gender. In 2009, weights for all 80 cm

girls in the reference population had a mean of 10.2 kg and standard

deviation of 0.8 kg. Weights are normally distributed. X~N(10.2,0.8)

Calculate z-scores that correspond to the following weights and interpret

them.

a.Ã‚Â Ã‚Â Ã‚Â 11 kg

b.Ã‚Â Ã‚Â Ã‚Â 7.9 kg

c.Ã‚Â Ã‚Â Ã‚Â 12.2 kg

#6

Suppose that the distance of fly balls hit to the outfield is normally

distributed with a mean of 250 ft and standard deviation of 50 ft.

a.Ã‚Â Ã‚Â Ã‚Â If X=distance in ft for a fly ball then X~___(___,____)

b.Ã‚Â Ã‚Â Ã‚Â If one fly ball is randomly chosen from this distribution, what is

the probability that this ball travelled fewer than 220 ft. Sketch the

graph. Scale the horizontal axis X. Shade the region corresponding to the

probability. Find the probability.

c.Ã‚Â Ã‚Â Ã‚Â Find the 80th percentile of the distribution of fly balls. Sketch

the graph, and write the probability statement.

#7

Facebook provides a variety of statistics on its Web site that detail the

growth and popularity of the site. On average, 28% of 18-34 year olds check

their Facebook profiles before getting out of bed in the morning. Suppose

this percentage follows a normal distribution with a standard deviation of

5%.

a.Ã‚Â Ã‚Â Ã‚Â Find the probability that the percent of 18-34 year olds who check

Facebook before getting out of bed in the morning is at least 30.

b.Ã‚Â Ã‚Â Ã‚Â Find the 95th percentile and express it in a sentence.

#8

Suppose that the distance of fly balls hit to the outfield (in baseball) is

normally distributed with a mean of 250 ft and a standard deviation of 50

ft. We randomly sample 49 fly balls.

a.Ã‚Â Ã‚Â Ã‚Â If X=average distance in feet for 49 fly balls, then

X~____(___,____)

b.Ã‚Â Ã‚Â Ã‚Â What is the probability that the 49 balls travelled an average of

less than 240 ft? Sketch the graph. Scale the horizontal axis for X. Shade

the region corresponding to the probability. Find the probability.

c.Ã‚Â Ã‚Â Ã‚Â Find the 80th percentile of the distribution of the average of 49

fly balls.

#9

Which of the following is NOT TRUE about the distribution for averages?

a.Ã‚Â Ã‚Â Ã‚Â Mean, median, and mode are equal

b.Ã‚Â Ã‚Â Ã‚Â Area under the curve is one

c.Ã‚Â Ã‚Â Ã‚Â Curve never touches the x-axis

d.Ã‚Â Ã‚Â Ã‚Â Curve is skewed to the right

#10

A typical adult has an average IQ score of 105 with a standard deviation of

0.065 g. If a vending machine is designed to accept coins whose weights

range from 5.111 g to 5.291 g, what is the expected number of rejected coins When 280 randomly selected coins are inserted into the machine?

Subject | Mathematics |

Due By (Pacific Time) | 04/12/2015 08:00 pm |

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